Nuprl Lemma : geo-gt-prim-implies-lt
∀e:EuclideanPlane. ∀a,b,c,d:Point. (ab>cd ⇒ |cd| < |ab|)
Proof
Definitions occuring in Statement :
geo-lt: p < q,
geo-length: |s|,
geo-mk-seg: ab,
euclidean-plane: EuclideanPlane,
geo-gt-prim: ab>cd,
geo-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
geo-lt: p < q,
geo-sep: a # b,
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
basic-geometry: BasicGeometry,
euclidean-plane: EuclideanPlane,
exists: ∃x:A. B[x],
uiff: uiff(P;Q),
true: True,
basic-geometry-: BasicGeometry-,
or: P ∨ Q,
squash: ↓T,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
geo-between: B(abc),
not: ¬A,
false: False
Latex:
\mforall{}e:EuclideanPlane. \mforall{}a,b,c,d:Point. (ab>cd {}\mRightarrow{} |cd| < |ab|)
Date html generated:
2020_05_20-AM-10_00_51
Last ObjectModification:
2020_01_27-PM-11_50_59
Theory : euclidean!plane!geometry
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